A bigger budget, up to a point, will give a more accurate result, but this can be partly overcome by doubling up for a week to let the system build some benchmarks and then cutting back to level out your overall spend.
You definitely don’t need hundreds of conversions to learn about the potential for lead generation. If on the other hand you want an end to end assessment of either ecommerce from click to cart to paid customer or lead to sales process to paid customer, then you need more planning, possibly more people (sales) and more budget. I would caution here that unless you are very confident about your salesforce, it is often wise to test end to end, especially if they are used to working different type of leads.
When calculating budget for a pilot, we usually give you a recommended range of budgets based on the available impressions/traffic and cost per click across a range of keywords.
Two things about a trial that are important are that a. Budgets are always a rule of thumb estimate, precision simply can’t be done and will waste a lot of effort. That doesn’t mean we can’t set a ceiling and guarantee not to go beyond it, but that we can’t be certain it is enough to answer your question, just that it is our best guess.